The goal of a vehicle simulator is to cause a human operator (the “operator” of the simulator) to feel (in as much as this is possible) what he or she would feel in the actual vehicle being simulated, were they operating the vehicle under the actual conditions that the simulator is then currently attempting to simulate. In circumstances where regulatory approval of the simulator is required (e.g. in the case of an aircraft simulator), a very high degree of fidelity of vehicle simulation is required in order to gain such approval, and to assist in the simulator actually be useful to its human operators to gain experience in operating the vehicle being simulated.
In order to achieve such a level of fidelity, the simulator's computer systems contain what is known as a “model” of the vehicle. This model of the vehicle attempts to mathematically describe various characteristics of the actual vehicle being simulated. The simulator's computer systems use this model to control the various other systems of the simulator (e.g. mechanical actuators that generate various accelerations experienced by the operator, simulator cabin visual display and audio generation systems, simulated vehicle instrumentation within the simulator cabin, etc.). The model must accurately mathematically describe the characteristics of the actual vehicle in order to have an accurate vehicle simulation, and it must do so preferably throughout the entire range of the intended simulated operating conditions, which typically encompasses the vehicle's entire operational envelope.
Typical simulation models of vehicle dynamics are what is known in the art as physically-based mathematical models. A physically-based mathematical model incorporates various explicit terms related to the vehicle physical's components and/or various physical phenomena that are believed to affect the vehicle's dynamics. (As it is impossible to perfectly mathematically model vehicle dynamics, there is no “one” physically-based model per vehicle. Many different physically-based models of a vehicle are possible that will satisfactorily enable vehicle simulation. Different simulator manufacturers and different model developers will create their own, slightly different models for using in modeling a vehicle.)
The reason why physically-based models are typically used in simulators is because they are generally capable of predicting the vehicle's dynamics under vehicle operating conditions to be simulated other than those operating conditions at which the physically-based models were validated. This predictive nature of such models is very important to model developers and simulator manufacturers.
The development of a physically-based model is very complex and time consuming; and particularly so for vehicles for which there is no comprehensive theory of motion. An example of such a vehicle is a helicopter; there being no comprehensive theory governing all aspects of helicopter flight mechanics. What this means is that a helicopter model developer, when developing a model for a particular helicopter, will incorporate into the model such terms as he or she believes to be appropriate, but that such a model will necessarily have parameters that are unknown (e.g. coefficients of terms already in the model, terms missing from the model—effectively having a coefficient of zero, etc.) and whose value must be determined in order to achieve the required level of fidelity of vehicle simulation. The values are conventionally determined through a time consuming iterative process (typically known as “tuning”) to achieve the required level of objective and subjective fidelity throughout the entire simulated helicopter flight envelope.
As an example, FIG. 1 illustrates a conventional method of physically-based vehicle model development. As a starting point the model developer(s) selects a physically-based mathematical model they believe to be appropriate (that will serve as a starting point of the development process) for the vehicle they are trying to simulate. What is “appropriate” in any particular instance is a function of experience, training and skill-level of the developer. Continuing with the example of a helicopter simulator, the model developer may start with a blade element model as a foundation for the simulation, and incorporate models representing physical phenomena such as rotor inflow and aerodynamic phase lag (ref 3, 4 & 5); fuselage and empennage aerodynamic (ref 4, 5 & 6); and aeroelastic parameters (ref 7 & 8). Each of these models includes parameters that may need to be determined empirically for a specific helicopter type.
Once the model has been constructed, it is populated with configuration data such as aerodynamic coefficients, mass properties, and aeromechanical data. As was discussed above, the model (being physically-based) will also include unknown parameters whose values need to be determined. Two examples of such unknown parameters in the helicopter example include (but are not limited to) inflow model parameters and downwash amplification factors for interactional aerodynamics. As was also discussed, the determination of the values of these parameters is accomplished via an iterative tuning process. Specifically, tuning is generally performed using brute-force methods, e.g. placing a large number of sweeping combinations of parameter values in the model and then assessing the impacts of such combinations on the model. For example, simulated time responses generated with a physically-based mathematical models for the various combinations of parameter values are compared with corresponding flight test data recorded during the flight of a real helicopter. The tuning process requires a lot of skill and experience from the model designers as, at each iteration, the model designers analyze the differences between the simulated time responses of the model and the corresponding vehicle (e.g. flight) test data, and determine new candidate parameter values for the next iteration. This process continues until an acceptable convergence between the simulated time responses and the corresponding vehicle test data is reached. If the tuning process is ineffective, i.e. there is no acceptable convergence between the simulated time response and the corresponding vehicle test data, then the physically-based mathematical model itself (as opposed to simply the values of its parameters) needs to be changed to incorporate terms for different physical components and/or phenomena, and the process restarted to tune that new model.
The decision of which parameters to adjust, either individually or in combination, is often based on physical reasoning, convenience or heuristics. Further the configuration data are not always known, in which case configuration data parameters may also need to be treated as tuning parameters. Thus, in the end, while the conventional development methodology of physically-based mathematical models for simulators yields satisfactory results, it is complex and time consuming,
A second conventional method (albeit completely separate from the physically-based model development process) is also used to develop vehicle models for use in simulating vehicle dynamics. This method may be referred to as the “state-space” method, as it involves the generation of a “state-space” model of the vehicle's dynamics. In a state-space model the vehicle is seen as a black-box, into which various inputs are sent and as a result of the functioning of which various outputs occur. Through various conventional techniques, a “state-space” model of the vehicle is created, such that the various inputs when sent into the model result in the appropriate outputs from the model. The actual physical components of the vehicle, their properties and the actual physical phenomena affecting the vehicle are neither expressly nor discretely modeled as part of the state-space model creation process (contrary to the case of a physically-based model). For an aircraft, for example, a typically state-space model consists of a small number of parameters that describe the dynamics of the vehicle as represented by the large set of time-response data.
A major drawback of a state-space model is the fact that such models can rarely be used for vehicle operating conditions other than those at which the model was created. This is because such state-space models do not have a good predictive capability beyond such vehicle operating conditions. Thus in the field of aircraft simulation, state-space models are conventionally only used for low-fidelity simulations or specialized applications requiring only limited flight envelope coverage (i.e. vehicle operating conditions limited to those similar to operating condition at which the state-space model was created). They are not used for high-fidelity, full-flight envelope simulations.
For example, if a state-space model is identified (created) from an aircraft's flight test data for an aircraft having and airspeed of 100 knots when travelling near sea level, one cannot assume that this model will also be valid for the same aircraft travelling at the same speed at an altitude of 10,000 feet. In the two cases the atmospheric pressure and density, and hence aerodynamic forces acting on the aircraft, will be different. (By contrast, a physically-based mathematical model for the same aircraft having properly-tuned based on data for the aircraft travelling at sea level would be able to predict the aircraft's behavior at 10,000 feet, as the physically-based model would incorporate mathematical terms related to physical laws including the effects of atmospheric pressure and density.)
It is common in the aircraft design and test and evaluation fields to express the flying qualities experienced by a human operator of the aircraft as stability and control coefficients, which are parameters of a state-space model. The stability and control coefficients describe the dynamic response of the vehicle to control inputs at a single operating condition without detailed knowledge the physical properties of the aircraft. Thus, even though state-space models are not used for full-envelope high-fidelity simulations, state-space models are useful in describing vehicle dynamics more compactly than the large set of time-response data that they represent. However, the traditional simulation model development method does not use stability and control coefficients during the design of the physically-based model. Therefore, the stability and control characteristics of the resulting physically-based model may not be accurate. Further improvements to the generation of aircraft simulation models are therefore desirable.